Which One Should I Imitate?

An individual repeatedly faces the same decision. Payoffs generated by his available actions are noisy. This individual forgets earlier experience and is limited to learn by observing current success of two other individuals. We select among behavioral rules that lead an infinite population of identical individuals in the long run to the expected payoff maximizing action. Optimal behavior requires learning by imitation. The second most successful in a sample must sometimes be imitated although the most successful will always be imitated with a higher probability. Inertia is optimal. When each individual follows an optimal rule, then the population evolves according to an aggregate monotone dynamic.